Symmetric strong vector quasi-equilibrium problems

In this paper, we introduce the symmetric strong vector quasi-equilibrium problem. We then demonstrate that the symmetric strong vector quasi-equilibrium problem is solvable under the suitable assumptions. As an application, we get an existence theorem of the strong saddle points of vector-valued functions. In addition, we give a characterization of vector-valued properly quasi-convex functions. This work was supported by the Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China     

Generalized vector quasi-equilibrium problems with applications

In this paper, we consider the generalized vector quasi-equilibrium problem with or without involving Φ-condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems. As applications of our results, we derive some existence results for a solution to the vector quasi-optimization problem for nondifferentiable functions and vector quasi-saddle point problem.     

On the symmetric vector quasi-equilibrium problems

In this paper we, using a particular technique, consider the symmetric vector quasi-equilibrium problems in the Hausdorff topological vector space. As applications of our existence theorem, a coincidence point theorem and the existence of vector optimization problem for a pair of vector-valued mappings are obtained. Moreover, we answer an open question raised by Fu in [J.Y. Fu, Symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl. 285 (2003) 708-713].     

Efficiency in vector quasi-equilibrium problems and applications

In this paper, we give sufficient conditions for the existence of efficient solutions of a generalized vector quasi-equilibrium problem in topological vector spaces. The motivations for introducing this problem come from practical problems in traffic networks and the optimal control theory for discrete-time dynamical systems. The main results of the paper are proven with the help of a strongly monotonic function which can be constructed from the data of the problem under consideration. Some notions of cone-semicontinuity of set-valued maps, weaker than the usual concepts of semicontinuity, are also used in our study. As applications, we obtain existence results in vector quasi-optimization problems, Stampacchia set-valued vector quasi-variational inequality problems and Pareto vector quasi-saddle point problems. All these results are different from the corresponding ones in the literature.     

Well-posedness for convex symmetric vector quasi-equilibrium problems

In this paper, the notion of a generalized Levitin–Polyak well-posedness is defined for symmetric vector quasi-equilibrium problems. Sufficient conditions are given for the generalized Levitin–Polyak well-posedness. Moreover, it is shown that the results can be refined in the convex case.     

Existences of solutions for generalized vector quasi-equilibrium problems

In the paper, existence theorems for two classes of generalized vector quasi-equilibrium problems are established by using a fixed point theorem and some examples are given to illustrate them. An application to vector quasi-optimization problems is shown. This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 60574073 and 10471142).     

Existence of solutions for generalized vector quasi-equilibrium problems

This paper deals with three classes of generalized vector quasi-equilibrium problems with or without compact assumptions. Using the well-known Fan-KKM theorems, their existence theorems for them are established. Some examples are given to illustrate our results.     

Approximate duality for vector quasi-equilibrium problems and applications

In this paper, we introduce new versions of ?-dual problems of a vector quasi-equilibrium problem with set-valued maps, and we give an ?-duality result between approximate solutions of the primal and dual problems. As the first application of the main result, we obtain an ?-duality for a vector quasi-equilibrium problem whose ?-solutions are understood in the sense of proper efficiency. The second application is devoted to an?-duality for a vector optimization problem with set-valued maps.     

New systems of generalized vector quasi-equilibrium problems in product FC-spaces

The notions of C _i (x)-FC-diagonally quasiconvex, C _i (x)-FC-quasiconvex and C _i (x)-FC-quasiconvex-like for set-valued mappings are introduced in FC-spaces without convexity structure. By applying these notions and a maximal element theorem for a family of set-valued mappings on product FC-space due to author, some new existence theorems of solutions for four new classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. These results improve and generalize some recent known results in literature to noncompact FC-spaces.     

Generalized abstract economy and systems of generalized vector quasi-equilibrium problems

The present paper is in two-fold. The first fold is devoted to the existence theory of equilibria for generalized abstract economy with a lower semicontinuous constraint correspondence and a fuzzy constraint correspondence defined on a noncompact/nonparacompact strategy set. In the second fold, we consider systems of generalized vector quasi-equilibrium problems for multivalued maps (for short, SGVQEPs) which contain systems of vector quasi-equilibrium problems, systems of generalized mixed vector quasi-variational inequalities and Debreu-type equilibrium problems for vector valued functions as special cases. By using the results of first fold, we establish some existence results for solutions of SGVQEPs.     

The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems

In this paper, the notion of the generalized Tykhonov well-posedness for system of vector quasi-equilibrium problems are investigated. By using the gap functions of the system of vector quasi-equilibrium problems, we establish the equivalent relationship between the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems and that of the minimization problems. We also present some metric characterizations for the generalized Tykhonov well-posedness of the system of vector quasi-equilibrium problems. The results in this paper are new and extend some known results in the literature.     

Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints

In this paper, we introduce several types of Levitin-Polyak well-posedness for a generalized vector quasi-equilibrium problem with functional constraints and abstract set constraints. Criteria and characterizations of these types of Levitin-Polyak well-posedness with or without gap functions of generalized vector quasi-equilibrium problem are given. The results in this paper unify, generalize and extend some known results in the literature.     

Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems

In this article, we study the parametric vector quasi-equilibrium problem (PVQEP). We investigate existence of solution for PVQEP and continuities of the solution mappings of PVQEP. In particular, results concerning the lower semicontinuity of the solution mapping of PVQEP are presented.      

Some existence results for solutions of generalized vector quasi-equilibrium problems

In this paper, we consider more general forms of generalized vector quasi-equilibrium problems for multivalued maps which include many known vector quasi-equilibrium problems and generalized vector quasi-variational inequality problems as special cases. We establish some existence results for solutions of these problems under pseudomonotonicity and u-hemicontinuity/ℓ-hemicontinuity assumptions.      

Upper semicontinuity of the solution maps in homogeneous vector quasi-equilibrium problems

The aim of this work was to study the solution maps in the vector homogeneous quasi-equilibrium problems. Here, we establish some sufficient and necessary conditions for upper semicontinuity of the solution maps in the vector homogeneous quasi-equilibrium problems. The results presented extend and improve the preceding results of Oetlli and Yen [Oetlli, W. and Yen, N.D., 1995, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems. In: F. Giannessi and A. Maugeri (Eds) Variational Inequalities and Network Equilibrium Problems (New York: Plenum Press)].     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理.作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理.     

Generalized vector quasi-equilibrium problems with applications to common fixed point theorems and optimization problems

In this paper, we first establish the existence theorems of generalized vector quasi-equilibrium problems. From these results, we establish the existence theorems of common fixed point theorems for two multivalued maps and mathematical programs with an equilibrium constraint as applications.     

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint corre- spondences are proved in FC-spaces.By using these equilibrium existence theorems,some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces.These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.